Abstract

NOTE: Everything under development here. Just showing ideas! :-)

The actual state of the robot can be described completely by:

speed (m/s)

direction (degree)

position (x,y - meter)

All sensors (gyro, acceleration, compass, odometry, perimeter signal strength, GPS, ...) can deliver certain information about the robot's state. However, each sensor is noisy (added with errors).
Sensor fusion is used to eliminate errors of each individual sensor. Each sensor gets a confidence weight that is automatically adjusted after reading the sensor by comparing its plausibility with the fusion result.

Position recalibration at perimeter border

Because odometry error increases over time, the robot needs to periodically recalibrate its exact position (get the error to zero). This works by detecting its exact position on the perimeter wire (using cross correlation).

Position detection: robot starts tracking the perimeter wire at arbitrary position until a high correlation with a subtrack of the perimeter tracking map is found. There it can stop tracking and knows its position on its perimeter tracking map.

Mapping and localization (SLAM)

The perimeter magnetic field could be used as input for a robot position estimation. However, as both the magnetic field map and the robot position on it is unknown, the algorithm needs to calculate both at the same time. Such algorithms are called 'Simultaneous Localization and Mapping' (SLAM).

Input to SLAM algorithm:

control values (speed, steering)

observation values (speed, heading, magnetic field strength)

Output from SLAM algorithm:

magnetic field map (including perimeter border)

robot position on that map (x,y,theta)

What is SLAM?

Example SLAM algorithms:

Particle filter-based SLAM plus Rao-Blackwellization: model the robot’s path by sampling and compute the 'landmarks' given the poses

Example implementation:
The idea is to use a particle filter that constantly generates a certain amount of 'guesses' (particles, e.g. N=50) where the robot can be (depending on the last position, control input, speed sensor and heading sensor measurements). Each 'particle' is evaluated by the perimeter field measurement...

strength precision is low in the center

same strenght values are located on rings

real measurements over a complete lawn

complete SLAM idea

... and the particle 'weight' is adjusted based on that. Bad particles are replaced by new particles with new guesses near the good guesses. This constantly produces particles with high probability of the robot's location.

Lane-by-lane mowing

In the lawn-by-lane mowing pattern, the robot uses a fixed course (accurate gyro + compass correction). When hitting an obstacle, the new course is added by 180 degree, so that the robot enters a new lane.

The robot always starts at the borders at an arbitrary choosen course, mowing lane by lane of a maximum length (distance determined by odometry). The maximum length ensures that the odometry position error does not get too high. At the perimeter, the robot can reduce the error to zero again (one axis). The arbitrary starting course ensures that even small gaps on the lawn are mown completely after a 2nd mowing session (where the robot started at another arbitrary course).

Robot turns 180 degree and enters a new lane

Mowing segment by segment

The maximum allowed yaw error (course error) can computed like this:

yaw error=arcsin(lane width error/lane length)

Assuming a lane length of 10m, and a lane width error of +/- 0.1m, the maximum allowed yaw error is:

yaw error=arcsin(0.1m/10m) = 0.5 degree

Assuming that robot moves at 0.4m/sec, the actual yaw error can be computed like this:

actual time needed = 10 meters / 0.4m/sec = 25 seconds

Actual yaw error (assuming gyro noise 0.005 degree/sec):

actual yaw error = 0.005 degree/sec * 25 seconds = 0.125 degree

Sensor logging

For PC data analysis, algorithm modelling and optimization, you can collect robot sensor data using pfodApp like this:

Connect your Android phone to the PC, if being asked on the phone choose 'Enable as USB device', so you phone shows as a new Windows drive on your PC.

On your PC, launch Windows Explorer and choose the new Android drive, browse to the 'pfodAppRawData' folder (for ArduRemote: 'ArduRemote' folder), and copy the data file to your PC (you can identify files by their Bluetooth name and date).